Analogs of Wiener’s Ergodic Theorems for Semisimple Lie Groups, Ii
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چکیده
X f dm, provided the action is ergodic. The main tool used in the proof of this result is Wiener’s maximal inequality, which asserts that the maximal function f ∗ β (x)= supt>0 |π(βt )f (x)| satisfies m{x : f ∗ β (x)≥ δ} ≤ (C/δ)‖f ‖L1(X). Consider the following generalization of the foregoing setup. LetG be a connected Lie group G, and let K be a compact subgroup. Assume there exists a G-invariant Riemannian metric on the homogeneous space S = G/K . The (bi-K-invariant) ball averages βt on G are defined to be the probability measures
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تاریخ انتشار 2000